## Background

In current physics, particle energy and photon energy are not related through equations. This is another example of the separation between the rules for physics between the classical and quantum worlds. The equation to relate energy to mass is Einstein’s famous E=mc^{2} and the equation for photon energy is Planck’s E=hf. There is no method in physics to describe the energy change from particles to photons or vice versa.

A fundamental rule in physics is the **conservation of energy**. Energy, within a defined volume, remains constant but it may change forms. In energy wave theory, particles have standing, longitudinal wave form. For photons, it is a transverse wave form. The energy for these waves are calculated from a fundamental energy wave equation, that is then derived into two types for longitudinal and transverse waves. This provides the mechanism to translate between the two types of wave forms using the conservation of energy principle.

Below, are two examples of how particle energy and photon energy interact and can be accurately modeled with energy wave equations.

## Example #1) Photon Release – Atoms

When an electron is captured into an atom, or moves to a lower orbital energy level, a photon is released. This is a transverse wave as a result of particle vibration as it settles into place. Each particle (proton and electron) has longitudinal, standing wave energy.

**Before an Electron is Captured by an Atom**

After the electron is captured, there is a change in longitudinal wave energy as these particles have destructive wave interference. **Energy is always conserved,** so this means that it is transferred to two, transverse waves that will travel in opposite directions. These transverse waves are photons.

**After Electron Captured by Atom**

**Transverse Energy – Photon**

A single electron and proton is hydrogen. At the first orbital, known as the Bohr radius (a_{0}), the Transverse Energy Equation was used to derive the Rydberg Constant (in joules). This is the energy of a photon that is released for an electron at the Bohr radius in hydrogen:

**Transverse Energy Equation (at Bohr Radius) – Rydberg Constant**

**Longitudinal Energy – Destructive Waves **

The energy for the photon is a result of a difference in longitudinal wave energy as two opposite phase particles destructively interfere, which is the case with a proton and electron. The energy difference in longitudinal wave form is:

The values E_{e} and r_{e} are the short form of the energy equation that is used for force. They are the energy of the electron and classical electron radius, respectively. Q is the particle count that is also used in the Force Equation. This energy equation is the basis of the Force Equation and its derivation. These values can be replaced by their wave constants to form the Longitudinal Energy Equation – Constructive Wave Interference Difference, where it is a function of two groups of particles with count Q, changing their distance (r). The equation above is simplified and then replaced by their wave constants.

**Longitudinal Energy Equation – Constructive Wave Interference Difference**

To solve for hydrogen and the Bohr radius, the same distances (r) are used in the equation above. However, two photons are created, so only half of this energy value is used to match one photon.

**E _{t }= 1/2 E_{l}.** The result from the change in longitudinal energy is

**-2.1799E-18 joules**. This is the same energy that is created in a new, transverse wave energy of the photon which is also

**-2.1799E-18 joules –**the Rydberg constant. Since there are two photons created, the transverse energy is 1/2 of the longitudinal energy. Energy is completed conserved, but it changes wave forms from longitudinal to transverse, or vice versa when a photon is absorbed (transverse to longitudinal).

## Example #2) Photon Release – Annihilation

When an electron interacts with a positron, it is known to annihilate and create two photons that match the rest energy of the electron. The section on annihilation describes the process and reason for this interaction, including why these two particles can also appear out of nowhere with pair production. Here, the process is described mathematically as the transfer of energy from wave forms.

**Before Annihilation – An Electron and Positron**

The positron is the anti-particle to the electron. It is identical to the electron in mass and charge. In wave theory, the only difference with this particle is that it is anti-phase on the longitudinal wave (180 degree phase shift). This causes destructive wave interference between these two particles.

After being attracted by destructive waves, the particles vibrate until they reach a resting position. This vibration causes two transverse waves – two photons. The particles (defined by their wave centers) are still there but without any standing waves to be measured as mass. They can be separated again later with a photon that is equal to or greater than the sum of their masses (pair production).

**After Annihilation – An Electron and Positron**

**Longitudinal Energy – Destructive Waves **

The conservation of energy applies again to this example. Two photons (E_{t}) are created from two electron masses (E_{l}). 2E_{t }= 2E_{l}** _{,}** or

**E**

_{t }=**E**. The longitudinal wave energy of the electron was calculated in the electron section and also shown as one of the fundamental physical constants, using the Longitudinal Energy Equation and wave constants.

_{l}

**Transverse Energy – Photon**

The two photons that are created from annihilation are calculated with the Transverse Energy Equation. This equation requires an initial distance (r_{0}) and a final distance (r). Infinity is used as the initial distance as the two particles initially start very far away from each other and can be modeled with infinity. The final distance for annihilation is called r_{C } where the “C” is Compton, since this is related to the Compton wavelength. Since annihilation is a phase-shift, which is 180 degrees (or half of the 360 degree rotation), the final resting position is half of the classical electron radius (r_{e}). This is the point where waves are completely destructive and a resting position for particles at minimal wave amplitude.

These distances are used in the Transverse Energy Equation.

The classical electron radius (r_{e}) is also solved for in terms of wave constants. These values are inserted and the equation can be solved.

**E _{t }=**

**E**. The photon energy calculated with the Transverse Energy Equation is

_{l}**8.1871E-14 joules**, which is identical to the mass of the electron, which is calculated with the Longitudinal Energy Equation at

**8.1871E-14 joules**. It shows that annihilation is a complete transfer of energy from standing waves of longitudinal wave energy to transverse energy. Conservation of energy.